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Find the integer n such that   

     ​\(10^n = 10^{3}\sqrt{\dfrac{10^{31}}{0.001}}\)

 Feb 14, 2019
edited by Guest  Feb 14, 2019
 #1
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10^n =10^3 x sqrt(10^34)

10^n =10^3 x 10^17 

10^n = 10^20    

n = 20

 Feb 15, 2019
edited by Guest  Feb 15, 2019
 #2
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We can simplify the radical to \(\frac{10^{31}}{10^{-3}}\), which equals 10^34

 

The square root of 10^34 is 10^17

 

10^17 * 10^3 = 10^20

 

So, n=20

 Feb 15, 2019

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